Tangent Lengths
Part of the Circles section of Coddy's Geometry journey. Lesson 49 of 62.
The right angle at the point of contact opens the door to the Pythagorean theorem. The radius and the tangent are the legs, and the segment from the center to the outside point is the hypotenuse.
Here the radius OT is 6 and OP is 10. The angle at T is 90° by the tangent rule, so TP² + 6² = 10², which gives TP² = 64 and TP = 8. The board will not use Pythagoras until it knows the angle at T is a right angle, so name the tangent rule first.
Challenge
TP is a tangent to circle O at T. The radius OT and the distance OP are given. Find the tangent length PT, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Circles
1Parts of a Circle
Center and RadiusChords and DiametersAll Radii Are EqualDiameter Is Two RadiiRecap: Parts of a Circle4Arcs and Sectors
Arc LengthArea of a SectorFind the Central AngleThe Missing Central AngleRecap: Arcs and Sectors7Angles in a Semicircle
Thales' TheoremThe Right Angle InsideIs That Enough?Semicircle With LettersRecap: Semicircles10Tangents
What a Tangent IsTangent and RadiusTangent LengthsTwo Tangents From a PointTangents With LettersRecap: Tangents2Circumference
Around the CircleUsing the DiameterRadius From CircumferenceCircumference With LettersRecap: Circumference5Radii Make Isosceles
Two Radii, One TriangleBase Angles From the CenterThe Angle at the CenterIsosceles With LettersRecap: Radii and Triangles8Angles on the Same Arc
Same Arc, Same AngleUsing the Same ArcSpot the Bow TieSame Arc With LettersRecap: Same Arc3Area of a Circle
The Area FormulaArea From the DiameterRadius From the AreaCircumference to AreaRecap: Area of a Circle6Inscribed Angles
Meet the Inscribed AngleHalf the Central AngleTwice the Inscribed AngleThe Big ArcInscribed With LettersRecap: Inscribed Angles